Finite Group Databasebeta

← #29708938

Subgroups — #29708938

Order 15616.

892 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454380C211yesmaximal, characteristic, complemented
2#421×D61C211yesmaximal, characteristic
3#21454334C211yesmaximal, characteristic
4#413×D61C211yesmaximal, characteristic
5#21447275C211yesmaximal, characteristic, complemented
6#21447274C211yesmaximal, characteristic, complemented
7#21447273C211yesmaximal, characteristic, complemented
8#21447272C211yesmaximal, characteristic, complemented
9#21447271C211yesmaximal, characteristic, complemented
10#21447270C211yesmaximal, characteristic, complemented
11#21447269C211yesmaximal, characteristic, complemented
12#344×D61C211yesmaximal, characteristic, complemented
13#21445544C211yesmaximal, characteristic, complemented
14H(3,ℤ/4)×D61C211yesmaximal, characteristic, complemented
15C61×#2080C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22#117×D61C2211yescharacteristic
23#16839790C2211yescharacteristic, complemented
24#16839789C2211yescharacteristic, complemented
25#16839788C2211yescharacteristic, complemented
26#16839787—22no—
27#16839784—22no—
28#16839780C2211yescharacteristic
29#16839779C2211yescharacteristic
30#16839778C2211yescharacteristic
31#16839777—22no—
32#104×D61—22no—
33#16839769—21no—
34#16839765—21no—
35#16839762—21no—
36#16839760—21no—
37#16839759C2211yescharacteristic
38#16839758C2211yescharacteristic
39#16839756C2211yescharacteristic
40#16839746C2211yescharacteristic
41#16839745—21no—
42#16839744C2211yescharacteristic
43#16839744C2211yescharacteristic
44#16839743—21no—
45#101×D61—21no—
46#100×D61—21no—
47#16839534C2211yescharacteristic, complemented
48#16839533C2211yescharacteristic, complemented
49#16839532C2211yescharacteristic, complemented
50#16839527C2211yescharacteristic, complemented
51#16839526C2211yescharacteristic, complemented
52#16839526C2211yescharacteristic, complemented
53#16839519C2211yescharacteristic, complemented
54#16839518C2211yescharacteristic, complemented
55#16839518C2211yescharacteristic, complemented
56C61×#424C2211yescharacteristic, complemented
57C61×#421C2211yescharacteristic
58C61×#416C2211yescharacteristic
59C61×#413C2211yescharacteristic
60C61×#344C2211yescharacteristic, complemented
61C61×#341C2211yescharacteristic, complemented
62C61×H(3,ℤ/4)C2211yescharacteristic, complemented
63C2×#11758226D411yescharacteristic
64C2×#11758222—21no—
65C2×#11758222C2311yescharacteristic
66C2×#11758224—21no—
67C2×#11758224D411yescharacteristic
68#41×D61—21no—
69#41×D61—21no—
70#41×D61—21no—
71#41×D61—21no—
72#41×D61—21no—
73#41×D61—21no—
74#41×D61—21no—
75#41×D61—21no—
76C2×Q8×D61D411yescharacteristic
77C2×D4×D61—21no—
78C2×D4×D61D411yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C2×#11758189—21no—
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×#11758189—21no—
90C2×#11758189—21no—
91C2×#11758189—21no—
92C2×#11758189—21no—
93M16×D61—21no—
94M16×D61—21no—
95M16×D61—21no—
96M16×D61—21no—
97M16×D61—21no—
98M16×D61—21no—
99M16×D61—21no—
100M16×D61—21no—
101M16×D61—21no—
102M16×D61—21no—
103M16×D61—21no—
104M16×D61—21no—
105C22×#92418C2311yescharacteristic
106C2×C8×D61—21no—
107C2×C8×D61—21no—
108C2×C8×D61—21no—
109#14519736C2311yescharacteristic
110#14519736C2311yescharacteristic
111#14519735—21no—
112#14519735—21no—
113#14519734—21no—
114#14519734D412yes—
115#14519733—21no—
116#14519733—21no—
117C4⋊C4×D61—21no—
118C4⋊C4×D61—21no—
119C22⋊C4×D61—21no—
120C22⋊C4×D61—21no—
121C42×D61—21no—
122C42×D61D412yes—
123C4⋊#92418—22no—
124#14519706—22no—
125#14519706—22no—
126#14519705—22no—
127#14519704—22no—
128#14519703—22no—
129#14519702—21no—
130#14519701—21no—
131#14519700—21no—
132#14519699—21no—
133#14519698—21no—
134#14519697—21no—
135#14519696—21no—
136#14519695—21no—
137#14519695—21no—
138#14519694—21no—
139#14519693—21no—
140#14519693—21no—
141C2×#41×C61C2311yescharacteristic
142C2×M16×C61C2311yescharacteristic
143C2×M16×C61C2311yescharacteristic
144C2×M16×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146#117×C61C2311yescharacteristic
147#117×C61C2311yescharacteristic
148C4⋊C8×C61—22no—
149#104×C61—22no—
150#103×C61—21no—
151#102×C61—21no—
152#101×C61—21no—
153#100×C61—21no—
154C23×D61—21no—
155C23×D61#4111yescharacteristic
156#41×C61—21no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160C2×Q8×C61C2×D411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—21no—
166C2×C22⋊D61—21no—
167C2×C22⋊D61—21no—
168C22×Dic61—21no—
169C22×Dic61#4111yescharacteristic
170#11758226—21no—
171#11758226—21no—
172#11758226—21no—
173#11758226—21no—
174Q8×D61—21no—
175Q8×D61—21no—
176Q8×D61—21no—
177Q8×D61—21no—
178#11758224—21no—
179#11758224—21no—
180#11758224—21no—
181#11758224—21no—
182#11758224—41no—
183#11758224—41no—
184#11758224—41no—
185#11758224—41no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190D4×D61—41no—
191D4×D61—41no—
192D4×D61—41no—
193D4×D61—41no—
194#11758222—21no—
195#11758222—21no—
196#11758222—21no—
197#11758222—21no—
198#11758222—41no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202C2×D244—21no—
203C2×D244C2×D411yescharacteristic
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—22no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
212C2×C4×D61—41no—
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61#4111yescharacteristic
218C2×C4×D61#4111yescharacteristic
219C2×C4×D61#4111yescharacteristic
220C2×C4×D61#4111yescharacteristic
221C2×C4×D61#4111yescharacteristic
222C2×C4×D61#4111yescharacteristic
223C2×C4×D61#4111yescharacteristic
224C2×C4×D61#4111yescharacteristic
225C2×Dic122—21no—
226C2×Dic122C2×D411yescharacteristic
227M16×C61—21no—
228M16×C61—21no—
229M16×C61—21no—
230M16×C61—21no—
231M16×C61—21no—
232M16×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C42×C61—21no—
244C42×C61C2×D412yes—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247#11758198—22no—
248#11758198—41no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251#11758196—22no—
252#11758196—41no—
253C4×Dic61—22no—
254C4×Dic61—21no—
255C4×Dic61—41no—
256C4×Dic61C2×D412yes—
257#11758194—21no—
258#11758194—21no—
259#11758194—21no—
260#11758194—21no—
261#11758194—21no—
262#11758194—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269#11758189—41no—
270#11758189—41no—
271#11758189—41no—
272#11758189—41no—
273#11758189—41no—
274#11758189—41no—
275#11758189—41no—
276#11758189—41no—
277#11758189—41no—
278#11758189—41no—
279C8×D61—41no—
280C8×D61—41no—
281C8×D61—41no—
282C8×D61—41no—
283C8×D61—41no—
284C8×D61—41no—
285C23×C61—21no—
286C23×C61C2×#4111yescharacteristic
287C22×D61—21no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—81no—
291C22×D61—82no—
292C22×D61#12311yescharacteristic
293C22×D61#12311yescharacteristic
294C22×D61#12311yescharacteristic
295C22×D61#12311yescharacteristic
296C22×D61#12611yescharacteristic
297C22×D61#12611yescharacteristic
298Q8×C61—21no—
299Q8×C61—21no—
300D4×C61—21no—
301D4×C61—21no—
302D4×C61—41no—
303D4×C61—41no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C22⋊D61—41no—
316C22⋊D61—41no—
317C22⋊D61—41no—
318C22⋊D61—41no—
319C22⋊D61—41no—
320C22⋊D61—41no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61#12311yescharacteristic
327C2×Dic61#12311yescharacteristic
328C2×Dic61#12311yescharacteristic
329C2×Dic61#12311yescharacteristic
330C2×Dic61#12611yescharacteristic
331C2×Dic61#12611yescharacteristic
332D244—21no—
333D244—21no—
334D244—41no—
335D244—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—82no—
343C4×D61—82no—
344C4×D61#12111yescharacteristic
345C4×D61#12111yescharacteristic
346C4×D61#12111yescharacteristic
347C4×D61#12111yescharacteristic
348C4×D61#12311yescharacteristic
349C4×D61#12311yescharacteristic
350C4×D61#12311yescharacteristic
351C4×D61#12311yescharacteristic
352C4×D61#12411yescharacteristic
353C4×D61#12411yescharacteristic
354C4×D61#12411yescharacteristic
355C4×D61#12411yescharacteristic
356C4×D61#12611yescharacteristic
357C4×D61#12611yescharacteristic
358C4×D61#12611yescharacteristic
359C4×D61#12611yescharacteristic
360Dic122—21no—
361Dic122—21no—
362Dic122—41no—
363Dic122—41no—
364C8×C61—41no—
365C8×C61—41no—
366C8×C61—41no—
367C8×C61—41no—
368#92418—41no—
369#92418—41no—
370#92418—41no—
371#92418—41no—
372#23649—611nomaximal, Sylow
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—81no—
376C22×C61C2×#12311yescharacteristic
377C22×C61C2×#12311yescharacteristic
378C22×C61C2×#12611yescharacteristic
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—82no—
387C2×D61—82no—
388C2×D61—81no—
389C2×D61#39711yescharacteristic
390C2×D61#39711yescharacteristic
391C2×D61#39711yescharacteristic
392C2×D61#39711yescharacteristic
393C4×C61—42no—
394C4×C61—41no—
395C4×C61—81no—
396C4×C61C2×#12111yescharacteristic
397C4×C61C2×#12311yescharacteristic
398C4×C61C2×#12411yescharacteristic
399C4×C61C2×#12611yescharacteristic
400Dic61—42no—
401Dic61—41no—
402Dic61—81no—
403Dic61#39711yescharacteristic
404Dic61#39711yescharacteristic
405Dic61#39711yescharacteristic
406Dic61#39711yescharacteristic
407#2905—611no—
408C2×#421—611no—
409#2896—611no—
410C2×#413—611no—
411#2080—611no—
412#2080—611no—
413#2080—611no—
414#2080—611no—
415#2080—611no—
416#2080—611no—
417#2080—611no—
418#2080D6111yescharacteristic, complemented
419C2×#344—611no—
420#1738—611no—
421C2×H(3,ℤ/4)—611no—
422C2×C61—21no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—81no—
426C2×C61C2×#39711yescharacteristic
427D61—21no—
428D61—21no—
429D61—21no—
430D61—21no—
431D61—81no—
432C22×#41—611no—
433C22×M16—611no—
434C22×M16—611no—
435C22×M16—611no—
436C22×M16—611no—
437C2×#117—611no—
438C2×#117—611no—
439#424—611no—
440#424—611no—
441#424—611no—
442#424—1222no—
443#424C2×D6111yescharacteristic, complemented
444#423—1222no—
445#421—611no—
446#421—611no—
447#421—611no—
448#421—1222no—
449#421C2×D6111yescharacteristic
450C2×#104—1222no—
451#419—1221no—
452#418—1221no—
453#417—1221no—
454#417—1221no—
455#416—611no—
456#416—611no—
457#416—611no—
458#416C2×D6111yescharacteristic
459#413—611no—
460#413—611no—
461#413—611no—
462#413—1221no—
463#413—1221no—
464#413C2×D6111yescharacteristic
465C2×#101—1221no—
466C2×#100—1221no—
467#344—611no—
468#344—611no—
469#344—611no—
470#344C2×D6111yescharacteristic, complemented
471#341—611no—
472#341—611no—
473#341—611no—
474#341C2×D6111yescharacteristic, complemented
475H(3,ℤ/4)—611no—
476H(3,ℤ/4)—611no—
477H(3,ℤ/4)—611no—
478H(3,ℤ/4)C2×D6111yescharacteristic, complemented
479C61#2364911yescharacteristic, complemented, Sylow
480C2×#41—611no—
481C2×#41—611no—
482C2×#41—611no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1221no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41C22×D6111yescharacteristic
494C22×Q8—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C23×C4—611no—
498C23×C4—1221no—
499C2×M16—611no—
500C2×M16—611no—
501C2×M16—611no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C2×M16—1221no—
523C2×M16C22×D6111yescharacteristic
524C2×M16C22×D6111yescharacteristic
525C2×M16C22×D6111yescharacteristic
526C22×C8—611no—
527C22×C8—1221no—
528C22×C8—1221no—
529C22×C8—1221no—
530C22×C8C22×D6111yescharacteristic
531#117—611no—
532#117—612no—
533#117—611no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117C22×D6111yescharacteristic
540#117C22×D6111yescharacteristic
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—612no—
546C2×C42—1221no—
547C4⋊C8—22no—
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—1222no—
551#104—22no—
552#104—1222no—
553#104—1222no—
554#104—1222no—
555#103—21no—
556#103—1221no—
557#103—1221no—
558#103—1221no—
559#102—21no—
560#102—1221no—
561#102—1221no—
562#102—1221no—
563#101—21no—
564#101—1221no—
565#101—1221no—
566#101—1221no—
567#100—21no—
568#100—1221no—
569#100—1221no—
570#100—1221no—
571C24—611no—
572C24—1221no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—1221no—
578#41—1221no—
579#41—1221no—
580#41—1221no—
581#41—1221no—
582#41—1221no—
583#41—1221no—
584#41—1221no—
585#41—1221no—
586#41—1221no—
587#41—1221no—
588#41—1221no—
589#41—2441no—
590#41—2441no—
591#41—2441no—
592#41—2441no—
593#41—2441no—
594#41—2441no—
595#41—2441no—
596#41—2441no—
597C2×Q8—611no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8D4×D6111yescharacteristic
604C2×D4—21no—
605C2×D4—611no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—2441no—
615C2×D4—2441no—
616C2×D4—2441no—
617C2×D4—2441no—
618C2×D4D4×D6111yescharacteristic
619C22×C4—21no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—1221no—
634C22×C4—1222no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—2441no—
639C22×C4—2441no—
640C22×C4—2441no—
641C22×C4—2441no—
642C22×C4—2441no—
643C22×C4C23×D6111yescharacteristic
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—1221no—
651M16—1221no—
652M16—1221no—
653M16—1221no—
654M16—1221no—
655M16—1221no—
656M16—2441no—
657M16—2441no—
658M16—2441no—
659M16—2441no—
660M16—2441no—
661M16—2441no—
662M16—2441no—
663M16—2441no—
664M16—2441no—
665M16—2441no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—2441no—
679C2×C8—2441no—
680C2×C8—2441no—
681C2×C8—2441no—
682C2×C8—2441no—
683C2×C8—2441no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—1222no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—2441no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—1222no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—2441no—
696C42—21no—
697C42—612no—
698C42—1222no—
699C42—1221no—
700C42—2441no—
701C42D4×D6112yes—
702C23—21no—
703C23—611no—
704C23—611no—
705C23—611no—
706C23—611no—
707C23—611no—
708C23—611no—
709C23—1221no—
710C23—4881no—
711C23—4882no—
712C23—2441no—
713C23—2441no—
714C23#41×D6111yescharacteristic
715Q8—21no—
716Q8—21no—
717Q8—1221no—
718Q8—1221no—
719Q8—2441no—
720Q8—2441no—
721D4—21no—
722D4—21no—
723D4—41no—
724D4—41no—
725D4—1221no—
726D4—1221no—
727D4—2441no—
728D4—2441no—
729D4—2441no—
730D4—2441no—
731D4—2441no—
732D4—2441no—
733D4—2441no—
734D4—2441no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—1222no—
763C2×C4—1221no—
764C2×C4—4882no—
765C2×C4—4882no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C2×D4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4#41×D6111yescharacteristic
778C2×C4#41×D6111yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#41×D6111yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—2441no—
786C8—2441no—
787C8—2441no—
788C8—2441no—
789C22—41no—
790C22—41no—
791C22—81no—
792C22—611no—
793C22—611no—
794C22—611no—
795C22—611no—
796C22—4881no—
797C22—4882no—
798C22—4882no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22#123×D6111yescharacteristic
807C22#123×D6111yescharacteristic
808C22#126×D6111yescharacteristic
809C4—42no—
810C4—41no—
811C4—81no—
812C4—611no—
813C4—611no—
814C4—611no—
815C4—611no—
816C4—4881no—
817C4—2442no—
818C4—2441no—
819C4#121×D6111yescharacteristic
820C4#123×D6111yescharacteristic
821C4#124×D6111yescharacteristic
822C4#126×D6111yescharacteristic
823C2—21no—
824C2—21no—
825C2—21no—
826C2—81no—
827C2—1221no—
828C2—1221no—
829C2—1221no—
830C2—1221no—
831C2—4881no—
832C2#397×D6111yescharacteristic
subgroupG/H
centerC4#124×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2080C2
socleC2×C61C2×#397
prime radicalC2×#41×D61C22
hypercenter#2080D61
hypocenterC61#23649
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2080

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21454380C2semidirect
5. #21447275C2semidirect
6. #21447274C2semidirect
7. #21447273C2semidirect
8. #21447272C2semidirect
9. #21447271C2semidirect
10. #21447270C2semidirect
11. #21447269C2semidirect
12. #344×D61C2semidirect
13. #21445544C2semidirect
14. H(3,ℤ/4)×D61C2semidirect
15. C61×#2080C2semidirect
23. #16839790C22semidirect
24. #16839789C22semidirect
25. #16839788C22semidirect
47. #16839534C22semidirect
48. #16839533C22semidirect
49. #16839532C22semidirect
50. #16839527C22semidirect
51. #16839526C22semidirect
52. #16839526C22semidirect
53. #16839519C22semidirect
54. #16839518C22semidirect
55. #16839518C22semidirect
56. C61×#424C22semidirect
60. C61×#344C22semidirect
61. C61×#341C22semidirect
62. C61×H(3,ℤ/4)C22semidirect
418. #2080D61semidirect
443. #424C2×D61semidirect
470. #344C2×D61semidirect
474. #341C2×D61semidirect
478. H(3,ℤ/4)C2×D61semidirect
479. C61#23649semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214543802
#421×D612
#214543342
#413×D612
#214472752
#214472742
#214472732
#214472722
#214472712
#214472702
#214472692
#344×D612
#214455442
H(3,ℤ/4)×D612
C61×#20802
#2364961